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PROFESSOR: Hello, everyone.

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Today we'll talk
about doping, which

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is the process of
intentionally adding impurities

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to a semiconductor
in order to change

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its electrical properties.

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Doping is a critical
process in the tech world.

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It's used in manufacturing
almost all semiconductor

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technologies today.

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Without doping, the solar
industry would not exist,

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but even though doping
is common today,

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the effects of impurities
confused semiconductor

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physicists in the 1950s, who
had trouble reproducing results.

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Eventually, they realized
that contamination levels,

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as low as 1 in a
billion, were vastly

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changing the electrical
properties of their samples.

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Today, we'll show
you how this works

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with a very simple experiment.

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We'll be measuring the
electrical conductivity

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of two silicon slabs
using an ohmmeter.

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One is doped with impurities,
phosphorus in our case,

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and the other is ultra-pure,
or what we call intrinsic.

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Let's go over our experiment.

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We'll start with
a slab of silicon,

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which we attach
metal contacts to.

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We'll use an ohmmeter,
that we connect

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to our sample with metal wires
to measure the conductivity.

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The conductivity
describes how well

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electricity can flow
through the material.

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The measured resistance
from our ohmmeter

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is related to the inverse
of the conductivity.

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The resistance also varies
according to the physical size

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and shape of our
sample, which adds

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a length over area term
to our equation, like so.

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Rearranging this equation,
gives is what we're looking for,

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the conductivity.

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Let's measure our samples,
and estimate the conductivity.

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Here are two samples, notice
that the doped sample looks

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identical to the intrinsic
one, or undoped sample.

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Because we've only
added trace impurities,

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the optical
properties are nearly

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identical between
the two samples.

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Let's hook up the ohmmeter
to the intrinsic sample.

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We can see that the resistance
is 130,000 ohms, which roughly

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corresponds to a conductivity of
0.0002 inverse ohm centimeters.

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Let's compare this
to the doped sample.

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We read a resistance
of 34 ohms, which

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corresponds to roughly 0.6
inverse ohm centimeters.

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So we can see that the dope
sample is around 3,000 times

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more conductive.

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But why would
adding small amount

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of our doping,
about one phosphorus

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atom for every
million silicon atoms,

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make our sample 3,000
times more conductive?

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On the periodic table,
we see that silicon

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is in the fourth
column, which means

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it has four valence electrons.

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Phosphorus, which is just
to the right in column five,

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has five valence electrons,
one extra compared to silicon.

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I'd also like to point
out boron in column three,

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with one fewer valence
electron than silicon.

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Later, I'll explain what happens
when you add boron as a dopant.

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We'll start with a
2D representation

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of a single silicon atom, with
the nucleus in the center,

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and its four valence electrons
in a silicon crystal,

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each silicon atom bonds to four
other silicon atoms around it.

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These rigid covalent
bonds, shown here,

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keep all of the electrons
effectively immobile, and are

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therefore, unable to aid
in the full electricity.

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Our intrinsic silicon,
or undoped example,

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has this material
structure, which

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is why it has a very
low conductivity.

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Let's quantify this relationship
between conductivity and mobile

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electrons.

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Conductivity is defined
as n times mu times e.

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n is a number of free
or mobile electrons.

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Again, in this drawing
of intrinsic silicon,

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all electrons are
covalently bonded so there

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are no mobile
electrons, and n is 0.

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The symbol mu represents the
mobility, a material parameter

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which you can look up in
a textbook, or online,

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and it basically describes how
well the charge can move around

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in the material.

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e is simply the amount of
charge that each mobile particle

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possesses, which in
all of our cases,

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is simply the charge
of an electron.

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So let's ask, what happens when
we add dopants like phosphorus

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and boron to the
silicon lattice?

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Now, let's dope our material
by replacing one of the silicon

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atoms with a phosphorus atom.

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First, we'll remove
a silicon atom,

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and for contrast, we'll dim
the background silicon lattice

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so we can emphasize
the dopant atom.

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Notice that the
inserted phosphorus atom

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has five valence
electrons, four of which

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form four covalent bonds with
their neighboring silicon atoms

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and are immobile.

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The fifth electron is not
bonded, and as a result,

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is free to move
around the lattice.

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When the negatively
charged electron leaves,

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the phosphorus dopant is
now positively charged.

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So we see that each
phosphorus atom that is added

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will contribute a
single mobile electron.

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So basically, in our case,
the number of mobile electrons

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is roughly equal to the
number of phosphorus

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atoms in our system.

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Now, let's remove
our phosphorus atom

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and put in an element with
three valence electrons,

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such as boron.

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We see here that boron lacks
the necessary valence electrons

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to form covalent bonds to its
four neighboring silicon atoms.

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This missing electron is
actually referred to as a hole,

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and is represented
by an H+ symbol.

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This hole acts as a
mobile positive charge

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because it can swap places with
neighboring covalently bonded

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electrons and move
around the crystal.

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When the positively charged
hole leaves its nucleus,

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the boron atom becomes
negatively charged.

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So we've demonstrated
that introducing

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atoms that have one more, or
one less, valence electron

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than silicon, can
add mobile charges

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and make the material
more conductive.

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In our examples, the
conductivity of silicon

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is proportional with the density
of either phosphorus or boron

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atoms.

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While phosphorus and boron
both affect the conductivity

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in a very similar
manner, they introduce

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mobile and static charges
of the opposite sign.

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Phosphorus introduces
mobile negative charges

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and immobile positive
charges, while boron

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creates mobile positive charges
and immobile negative charges.

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This subtle difference between
phosphorus and boron dopants

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will be crucial
in our final video

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when we discuss
solar cell operation.

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Today we learned that
we can use doping

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to control the conductivity
of semiconductors

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by changing the number of
mobile charges in the material.

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When we look at the
range of conductivities

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that silicon possess,
it is truly amazing.

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Through doping, we have
a very powerful way

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of varying the conductivity
of semiconductors.

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This is something that is
not possible in other classes

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of materials, like metals.

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Next time, we'll
be discussing how

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light can be used to generate
mobile charges in silicon,

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so watch our next video.

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I'm Joe Sullivan, and
thanks for watching.

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